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Hodge Theory and Complex Algebraic Geometry I by Claire Voisin, Leila Schneps

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11

Hodge Classes

The last two chapters of this volume form an introduction to a subject which is one of the major themes of the second volume: the interaction between algebraic cycles and the Hodge theory of a projective smooth complex variety. Here, we remain in the framework of Kähler geometry; thus we consider analytic cycles, which are combinations with integral coefficients of irreducible closed analytic subsets.

The first object associated to an analytic cycle in a compact complex manifold is its homology class. More generally, without any compactness hypothesis, we can define the cohomology class [Z] ∈ H2k(X, image) of an analytic subset of ...

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